Edelweiss Applied Science and Technology 
ISSN: 2576-8484 
Vol. 8, No. 6, 8497-8505 
2024 
Publisher: Learning Gate 
DOI: 10.55214/25768484.v8i6.3823 
© 2024 by the authors; licensee Learning Gate 

© 2024 by the authors; licensee Learning Gate 
* Correspondence:  Thaer.h@comed.uobaghdad.edu.iq 

 
 
 
 
 

Using count regression models to investigate the most important economic 
factors affecting divorce in Iraq 

 
Thaer Hasimabdulmuttaleb1*, Hayder Raaid Talib2, Ameer Kamil Hazmah3 
1University of Baghdad/College of Medicine; Thaer.h@comed.uobaghdad.edu.iq (T.H.). 
2University of sumer / College of Administration & Economics; haider.raid@uos.edu.iq (H.R.T.). 
3Middle Technical University / Technical Medical Institute - almansoor; Ameeralkk@mtu.edu.iq (A.K.H.). 

 

 
Abstract: The two most popular models inwell-known count regression models are Poisson and 
negative binomial regression models. Poisson regression is a generalized linear model form of 
regression analysis used to model count data and contingency tables. Poisson regression assumes the 
response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be 
modeled by a linear combination of unknown parameters. Negative binomial regression is similar to 
regular multiple regression except that the dependent (Y) variables an observed count that follows the 
negative binomial distribution. This research studies some factors affecting divorce using Poisson and 
negative binomial regression models. The factors are unemployment rate, inflation and Gini coefficient. 
The data were taken from the website of the Statistics Center for the years 2002 to 2023.Under the 
Poisson regression model, each factor has been reported to have an effect on the divorce rate. The two 
factors of inflation and unemployment had a direct effect and income inequality factors had an inverse 
effect on the divorce rate. But, under the negative binomial regression model, only inflation has an effect 
on the number of divorces. It is worth noting that according to the AIC values, the negative binomial 
regression model has a better fit than the Poisson regression model because its AIC value is lower. 
Keywords: Maximum Likelihood Estimation, Negative binomial regression, Poisson regression. 

 
1. Introduction  

This research studies some factors affecting divorce using count regression models. Divorce and 
family dissolution are global issues that are related to various socio-economic, demographic and spatial 
variables. In the past decades, the divorce rate has increased dramatically in different countries, 
including Iraq. Rapid economic development, social transformation, and modernization have directly led 
to profound cultural changes in marriage and marital instability (Pamukcu and at all 2014). One of the 
main problems of the modern age is the dramatic change in the family, especially marital relations. The 
dissolution of the traditional family composition, the difference between generations, the significant 
increase in the divorce rate and the expansion of cohabitation have become hard and fast realities today. 
These reforms are more related to social-based personal motivations, the most important of which are 
financial disturbances in the family, increasing women's financial independence, and changing the role of 
women in the family (Soleymanov 2010). 

Psychological research in the field of family shows that several factors play a role in the separation 
of couples and the collapse of the family foundation, among which economic problems such as inflation, 
unemployment, and class differences are known as the most important factors. Naturally, when a family 
faces difficulties in providing its most basic needs, it will not be successful in controlling and managing 
other parts of life and psychological and emotional needs. Financial capabilities meet people's low-level 
needs, and if people feel financially secure, they will also meet their high-level needs. This is despite the 
fact that if the basic needs are not even partially met, the next needs will not be formed. In most cases, 
divorce also happens due to lack of financial stability in life (Aghajanian and Thompson 2013). 



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2. Poisson Regression 
Poisson regression is similar to regular multiple regression except that the dependent (Y) variable is 

an observed count that follows the Poisson distribution. Thus, the possible values of Y are the 
nonnegative integers: 0, 1, 2, 3, …. It is assumed that large counts are rare. Hence, Poisson regression is 
similar to logistic regression, which also has a discrete response variable. However, the response is not 
limited to specific values as it is in logistic regression. 

An example of the proper application of Poisson regression is the study of how the number of 
divorces in a year is related to influencing factors, including economic factorsAnother example is the 
study of how the number of bacterial colonies is related to different environmental conditions and 
dilutions.Another example is the number of failures for a certain machine at various operating 
conditions. Still another example is vital statistics concerning infant mortality or cancer incidence 
among groups with different demographics. 
 
2.1. The Poisson Distribution 

The Poisson distribution models the probability of y events (i.e., failure, death, or existence) with 
the formula 

Pr(Y = y|μ) =
e−μμy

y!
;    y = 0,1,2, …                (1) 

Notice that the Poisson distribution is specified with a single parameter 𝜇. This is the mean 
incidence rate of a rare event per unit of exposure. Exposure may be time, space, distance, area, volume, 
or population size. Because exposure is often a period of time, we use the symbol t to represent the 
exposure. When no exposure value is given, it is assumed to be one. 

The parameter 𝜇 may be interpreted as the risk of a new occurrence of the event during a specified 
exposure period, t. The probability of y events is then given by 

Pr(Y = y|μ, t) =
e−μt(μt)y

y!
;    y = 0,1,2, …                 (2) 

The Poisson distribution has the property that its mean and variance are equal. 

In Poisson regression, we suppose that the Poisson incidence rate 𝜇 is determined by a set of k 
regressor variables (the X’s). The expression relating these quantities is 

μ = t exp(β1X1 + β2X2 + ⋯ + βkXk)                     (3) 
Note that often, 𝑋1  ≡  1 and 𝛽1 is called the intercept. The regression coefficients 𝛽1, 𝛽2, ⋯ , 𝛽𝑘 are 

unknown parameters that are estimated from a set of data. Their estimates are labeled 𝑏1, 𝑏2, ⋯ , 𝑏𝑘. 

Using this notation, the fundamental Poisson regression model for an observation 𝑖 is written as 

Pr(Y = yi|μi, ti) =
e−μiti(μiti)

yi

yi!
                         (4) 

Were 

μi = tiμ(xi
′β) = ti exp(β1X1i + β2X2i + ⋯ + βkXki)            (5) 

That is, for a given set of values of the regressor variables, the outcome follows the Poisson 
distribution. We assume that t=1 (one year). 
 
2.2. Maximum Likelihood Estimation of Parameters 

We use the method of maximum likelihood estimation to estimate the parameters of the Poisson 

regression model. The likelihood function is based on Poisson distribution with parameter 𝜇 and then 

𝛽's are estimated through the link function. 

The likelihood function of 𝑦𝑖 , 𝑦2, … , 𝑦𝑛 is 

L(y, β) = ∏ Pr(Y = yi|μi)

n

i=1

=
(∏ μi

yin
i=1 )(exp(− ∑ μi

n
i=1 ))

∏ yi!
n
i=1

                      (6) 

And the logarithm of likelihood function is 



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log[L(y, β)] = ∑ yi log[μi]

n

i=1

− ∑ μi

n

i=1

− ∑ log(yi!)

n

i=1

.                         (7) 

The parameter μi can be related to β's through the link function 

μi = g−1(xi
′β). 

After choosing the proper link function, the log-likelihood function can be maximized using some 

numerical optimization techniques for a given set of data. Let �̂� be the obtained maximum likelihood 

estimator of 𝛽. Then the fitted Poisson regression model is 

ŷi = g−1(xi
′β)                                       (8) 

In case of identity link, 

ŷi = g−1(xi
′β) = xi

′β                           (9) 
In the case of log-link, 

ŷi = g−1(xi
′β) = exp(xi

′β)                 (10) 
Of course, the likelihood equations may be formed by taking the derivatives with respect to each 

regression coefficient and setting the result equal to zero. Doing this leads to a set of nonlinear 
equations that admits no closed form solution. Thus, an iterative algorithm must be used to find the set 
of regression coefficients that maximum the log-likelihood. Using the method of iteratively reweighted 
least squares, a solution may be found in five or six iterations. However, the algorithm requires a 
complete pass through the data at each iteration, so it is relatively slow for problems with a large 
number of rows. With today’s computers, this is becoming less and less of an issue. 
 
2.3. Distribution of the MLE’s 

Applying the usual maximum likelihood theory, the asymptotic distribution of the maximum 
likelihood estimates (MLE’s) is multivariate normal. That is, 

β̂ ∼ N(β, βVβ̂)                                   (11) 

Were  

Vβ̂ = (∑ μi

n

i=1

xixi
′)

−1

                           (12) 

Remember that in the Poisson model the mean and the variance are equal. In practice, the data 
almost always reject this restriction. Usually, the variance is greater than the mean a situation called 
overdispersion. The increase in variance is represented in the model by a constant multiple of the 
variance covariance matrix. That is, we use 

Vβ̂ = ϕ (∑ μi

n

i=1

xixi
′)

−1

                              (13) 

where 𝜙 is estimated using 

ϕ̂ =
1

n − k
∑

(yi − μ̂i)
2

μ̂i

n

i=1

.                               (14) 

 
2.4. Testing of Hypothesis 

The test of hypothesis is constructed as model deviance which is based on a large sample test using 
the likelihood ratio test statistic. The model deviance is defined as 

𝜇∗(𝛽) = 2 𝑙𝑜𝑔(𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑 𝑚𝑜𝑑𝑒𝑙) − 2 𝑙𝑜𝑔(�̂�)                 (15) 
where the saturated model is based on all the p parameters of the model, and it fits the data 

perfectly.The statistic μ∗(β) has approximately χ2(n − p) distribution when n is large. The large value 

of 𝜇∗(𝛽)indicates that the model is not correctly fitted to the given data whereas small values of 𝜇∗(𝛽) 



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indicating thatmodel is well fitted to the given set of data in the sense that it is as good as the saturated 
model. 
For the hypothesis test  

HO: βi = 0versusH1: βi ≠ 0 (or H1 ∶  βi >  0𝑜𝑟 H1 ∶ βi < 0), 

z =
βî − β0

ASE
=

βî

ASE
                                      (16) 

where βo is the hypothesized value of β under the null hypothesis (i.e., βo = 0) and ASE = √Vβ̂[i, i] 

is the asymptotic standard error of β̂. If the null hypothesis is true, then the statistic z is approximately 
standard normal  

z =
βî

ASE
≈ N(0,1).                                   (17) 

An estimated parameter divided by it’s ASE and squared is a “Wald Statistic”. It means that  

z2 = (
βî

ASE
)

2

≈ χ2(1)                                 (18) 

𝑧2 has (asymptotically) a chi-squared distribution with df = 1. Wald statistics are usually provided 
on computer output, along with p–values.  
 
3. Negative Binomial Regression 

Negative binomial regression is similar to regular multiple regression except that the dependent (Y) 
variables an observed count that follows the negative binomialdistribution. Thus, the possible values of 
Y are thenonnegative integers: 0, 1, 2, 3, and so on.Negative binomial regression is a generalization of 
Poisson regression which loosens the restrictiveassumption that the variance is equal to the mean made 
by the Poisson model. The traditional negativebinomial regression model, commonly known as NB2, is 
based on the Poisson-gamma mixture distribution.This formulation is popular because it allows the 
modelling of Poisson heterogeneity using a gammadistribution (for more details see Cameron and 
Trivedi (2013) and Hilbe (2014)). 
 
3.1. The Negative Binomial Distribution 

The Poisson distribution may be generalized by including a gamma noise variable which has a mean 

of 1 and a scale parameter of ν. The Poisson-gamma mixture (negative binomial) distribution that 
results is 

Pr(Y = yi|μi, α−1) =
Γ(yi + α−1)

Γ(yi + 1)Γ(α−1)
(

α−1

α−1 + μi
)

α−1

(
α−1

α−1 + μi
)

yi

         (19) 

Where 𝜇𝑖 = 𝑡𝑖𝜇,   𝛼 =
1

𝑣
. The parameter μ is the mean incidence rate of y per unit of exposure. 

Exposure may be time, space, distance, area, volume, or population size. Because exposure is often a 

period of time, we use the symbol 𝑡𝑖to represent the exposure for a particular observation. When no 

exposure given, it is assumed to be one.The parameter μ may be interpreted as the risk of a new 
occurrence of the event during a specified exposure period, t.The results below make use of the 
following relationship derived from the definition of the gamma function 

log (
Γ(yi + α−1)

Γ(α−1)
) = ∑ log(j + α−1)

yi−1

j=0

          (20) 

In negative binomial regression, the mean of y is determined by the exposure time t and a set of k 
regressor variables (the x’s). The expression relating these quantities is 

μi = exp(log(ti) + β1x1i + β2x2i + ⋯ + βkxki)           (21) 



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Often, 𝑥1 =  1, in which case 𝛽1 is called the intercept. The regression coefficients 𝛽1, 𝛽2, … , 𝛽𝑘 are 
unknownparameters that are estimated from a set of data. Their estimates are symbolized as 

𝑏1, 𝑏2, … , 𝑏𝑘. 
 
3.2. Maximum Likelihood Estimation 

Suppose that 𝑌1, … , 𝑌𝑛 is a random sample of negative binomial distribution. The regression 
coefficients are estimated using the method of maximum likelihood. Cameron (2013, page81) gives the 
logarithm of the likelihood function as 

l(β) = ∑ [log(Γ(yi + α−1)) − log Γ(α−1) − log(Γ(yi + 1))

n

i=1

− α−1 log(1 + αμi) − yi log(1 + αμi)

+ yi log(α) + yi log(μi)]         (22) 
The first derivatives of 𝑙(𝛽) were given by Cameron (2013) and Lawless (1987) as 

∂l(β)

∂βj
= ∑

xij(yi − μi)

1 + αμi

n

i=1

,           j = 1,2, … , k       (23) 

And  

∂l(β)

∂α
= ∑ {α−2 (log(1 + αμi) − ∑

1

j + α−1

yi−1

j=0

) +
yi − μi

α(1 + αμi)
}

n

i=1

        (24)  

Equating the gradients to zero gives the following set of likelihood equations 

∑
xij(yi − μi)

1 + αμi
= 0

n

i=1

,           j = 1,2, … , k     (25) 

and 

∑ {α−2 (log(1 + αμi) − ∑
1

j + α−1

yi−1

j=0

) +
yi − μi

α(1 + αμi)
} = 0

n

i=1

       (26) 

 
3.3. Distribution of the MLE’s 

Cameron (2013) gives the asymptotic distribution of the maximum likelihood estimates as 
multivariatenormal as follows 

[β̂
α̂

] ∼ N [
V(β̂) Cov(β̂, α̂)

Cov(β̂, α̂) V(α̂)
]     (27) 

Were 

V(β̂) = [∑
μi

1 + αμi
xixi

′

n

i=1

]

−1

,     Cov(β̂, α̂) = 0       (28) 

V(α̂) = ∑ {α−4 (log(1 + αμi) − ∑
1

j + α−1

yi−1

j=0

)

2

+
μi

α2(1 + αμi)
}

−1
n

i=1

    (29) 

 
4. Akaike’s Information Criterion 

The Akaike’s information criterion is used to determine the superiority between thedistributions or 
models to the data, denoted by the symbol AIC, and can be calculated as follows: 

AIC = −2 log (L(θ̂)) + 2p   (30) 



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Where 𝐿(𝜃) is the maximum value of the likelihood function for the estimation of the parameters 
and p is the number of model parameters. Among the fitted models, the distribution where AIC is lower 
than the others is preferred. 
 
4.1. Really Data 

Factors affecting the occurrence of divorce have been one of the main axes investigated in 
sociological researches in recent years, and from the point of view of social and psychological experts, 
many economic, social and cultural, psychological, behavioral and even physical reasons are involved in 
leading a relationship to divorce. Above all, there are economic problems. By looking at the statistics 
and comparing it with the phenomenon of divorce, we find out that the statistics of cohabitation collapse 
has grown significantly along with inflation and unemployment. 

The disproportion of salaries and wages with the growth of prices and annual inflation and the 
aggravation of the gap between expenses and income have faced many harms to the joint life, and 70% 
inflation, the increase in food prices, and the high cost of housing and rent are among the factors 
influencing the end of the joint life.Scientific findings also show that economic problems affect 
practically all aspects of life and individual, family and social needs of people. Therefore, psychologists 
believe that in a society where the economy is in trouble, it is very ridiculous to talk about why the 
divorce rate is increasing; Because there are still more basic needs to be met. 

The research results and findings indicate that the probability of divorce is higher in women than in 
men and in urban areas than in rural areas. Education has a negative relationship with the probability of 
divorce. Also, unemployment and job instability have a positive and strong relationship with the 
possibility of divorce. 

Therefore, research entitled "Sociological investigation of economic factors affecting the growth of 
divorce rate" shows that the most important factor in the growth of divorce rate is due to 
mismanagement at the macroeconomic level. Therefore, there is a relatively strong and inverse 
relationship between the increase in the divorce rate and the economic stability of families, and as 
economic problems increase, divorce grows. 

Job instability of the head of the family and increasing and sudden inflations and income inequality 
are part of the economic factors affecting the growth of divorce. Another article entitled "Analysis of 
economic-social characteristics related to divorce in Iraq" emphasizes the positive relationship between 
unemployment and increasing the probability of divorce, and on the other hand, employment 
contributes to the stability and continuity of life together. "According to this research, having a job 
reduces the probability of experiencing divorce by 23%, but being unemployed or looking for a job 
increases the probability of being divorced by 51%, which is reduced to 39% by controlling other 
variables. Also, having income without work reduces the probability of divorce by 32%. Being in a poor 
socio-economic status increases the probability of divorce by 44% and by controlling other variables, 
this issue increases to 46%. Also, average socio-economic status increases the probability of divorce by 
23%. According to the above researches, the economic events of 2018 and later led to the increasing 
growth of inflation, unfavorable job situation, wave of layoffs and economic recession and heavy 
inflation in the housing sector and gradually weakened the foundation of the family and increased the 
number of divorces in the last one or two years. In the end, the rise of the dollar and the heavy inflation 
that followed caused the final blow to the shaky body of the family economy, so that divorce reached its 
peak in the early months of this year. 

Therefore, in this research, we try to measure the effect of three factors: unemployment, inflation 
and income inequality on the divorce rate in Iraq.Table 1 show the values of unemployment rate, 
inflation, Gini coefficient and the number of registered divorces people in Iraq for the years 2002 to 
2023. 

 
 
 
 
 
 



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Table 1. 
The values of unemployment rate, inflation, Gini coefficient divorces people in Iraq for the years 2001 to 2023. 

Year Unemployment (%) Inflation (%) Gini coefficient (%) Divorces per 100 thousand 
2002 13.1 15.8 41.91 67256 
2003 11.6 15.6 41.56 72359 
2004 10.4 15.2 40.01 63125 
2005 11.2 10.4 40.02 84241 
2006 11.1 11.9 40.0 94040 
2007 10.3 18.4 40.45 99852 
2008 10.2 25.4 38.56 110510 
2009 12.0 10.8 39.41 125747 
2010 13.8 12.4 38.11 137200 
2011 12.1 21.5 37.41 142841 
2012 12.0 30.5 38.33 150324 
2013 10.3 34.7 39.40 155369 
2014 10.6 15.6 39.91 163569 
2015 10.8 11.9 39.54 163765 
2016 12.2 9.0 40.46 181049 
2017 11.9 9.6 39.84 182623 
2018 11.8 31.2 40.93 179374 
2019 10.1 41.2 39.92 178812 
2020 9.6 47.1 40.06 187553 
2021 9.2 46.2 39.38 203904 
2022 9.1 45.8 38.77 204301 
2023 8.2 40.7 36.14 202183 

 
Now we intend to measure the impact of each of these three economic factors on the divorce rate by 

fitting the Poisson and negative binomial regression models.This task was done using R software and 
its results are listed in Table 2 and Table 3. 
 

Table 2. 
Results of fitting poisson regression model to data. 

Coefficients Estimate Std. error z value Pr(>|z|) AIC 
Intercept 1.380e+01 1.841e-02 749.77 <2e-16 ***  

21291 Unemployment 2.189e-02 5.909e-04 37.04 <2e-16 *** 
Inflation 1.368e-02 5.951e-05 229.89 <2e-16 *** 
GF -6.354e-02 4.497e-04 -141.31 <2e-16 *** 

 
Table 3. 
Results of fitting negative binomial regression model to data. 

Coefficients Estimate Std. error z value Pr(>|z|) AIC 
Intercept 14.411 2.086 6.908 4.91e-12 ***  

537.33 Unemployment 0.023 0.063 0.370 0.711 
Inflation 0.012 0.006 1.993 0.0463 * 
GF -0.078 0.050 -1.567 0.117 

 
The following results can be expressed according to Table 2. 

1) According to the p-value, all three variables are significant at the 0.01 error level, which means 
that each variable of unemployment rate, inflation and income inequality has an effect on 
divorces. 

2)   We consider the results of the above table in the row of unemployment rate. The regression 
coefficient is equal to 2.189e-02. Its positivity indicates a direct relationship between 



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unemployment rate and divorces. In other words, the higher the unemployment rate, the higher 
the average of divorces. 

3) The regression coefficient number for the inflation variable is equal to 1.368e-02. Its positivity 
indicates a direct relationship between inflation rate and divorces. In other words, the higher the 
inflation, the higher the higher the average of divorces. 

4) The noteworthy point is that the regression coefficient number for the Gini coefficient variable 
is equal to -6.354e-02, which is a negative number. Its negativity indicates the inverse 
relationship between the Gini coefficient as an indicator of income inequality and divorce. In 
other words, the higher this index is, the lower the average number of divorces. 

According to Table 3, it can be said that only the coefficient of the intercept and the coefficient of 
the inflation factor are significant, which means that among the three factors of unemployment, inflation 
and income inequality, only inflation has an effect on the number of divorces. It is worth noting that 
according to the AIC values, the negative binomial regression model has a better fit than the Poisson 
regression model because its AIC value is lower. Therefore, the results of Table 3 are preferable. 

 
5. Summary and Conclusion 

In this research, we seek to find the relationship between unemployment, inflation and income 
inequality and the average number of divorces in Iraq by using Poisson and negative binomial 
regression models. The results were deferent. The results ofPoissonregression model show that there is 
a significant relationship between the unemployment rate and the divorce rate, and with the increase in 
the unemployment rate, the average number of divorces increases. The results of this research on 
unemployment due to the existence of a significant positive relationship between the unemployment rate 
and divorce are similar to the results of most of the studies conducted abroad, and in fact, the 
experimental findings are a confirmation of the theoretical foundations used in this research. We also 
saw that the relationship between inflation rate and divorce is direct and significant.  

The results of negative binomial regression modelshow thatonly inflation has an effect on the 
number of divorces.Both models show that the inflation factor is an influencing factor on the number of 

divorces.Stability of inflation can be a factor that, although it will reduce economic growth in the short 
term, but in the long term, it will have significant effects on economic growth, and as a result, we will 
have a reduction in divorce and social damage. 
 
Copyright:  
© 2024 by the authors. This article is an open access article distributed under the terms and conditions 
of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). 
 
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https://creativecommons.org/licenses/by/4.0/


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Edelweiss Applied Science and Technology 
ISSN: 2576-8484 

Vol. 8, No. 6: 8497-8505, 2024 
DOI: 10.55214/25768484.v8i6.3823 
© 2024 by the authors; licensee Learning Gate 

 

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